At a guess, the same groundwork hasn't been laid over time.
The history of feminism in the west is very, very closely tied with the European Enlightenment period, when these ideas first started floating around, particularly, among the German and Italian nobility. From there it developed further, and women's rights began to evolve together alongside other Enlightenment ideas as they snowballed from the Corsican Revolution and into the French Revolution. Along with the Declaration of the Rights of Man came the Declaration of the Rights of Woman - while not taken as seriously by its contemporaries, it and works like it began to lay the groundwork from which the education of women, women's suffrage, women's property rights and all of that has flowed over the succeeding centuries.
To a significant extent, though not an exclusive one, it's taken a better hold in the west because it's had more time. Far be it from me to suggest that it's just something that will eventually happen in the fullness of time - I despise that sort of Whiggishness - but sometimes things do take time to change, and the West has a bit of a head start. More work needs to be done, pretty much everywhere, before we reach the ideal of effective and real universal equality.